§ C-20 Radical Polymerization of Ethylene & Polyethylene Chain Growth (Grade 9–11 · Polymerization)
Chain-growth polymerization n CH₂=CH₂ → (–CH₂–CH₂–)ₙ, sp² → sp³ hybridization shift, molar mass Mₙ, and coil radius R_g. Cleaving each monomer π-bond releases 93 kJ/mol of energy, zipping thousands of ethylene units into a flexible sp³ polyethylene macromolecule.
Theory Summary & Scientific Mechanism
Chain-growth polymerization is the sequential addition of unsaturated monomer molecules M (such as ethylene CH₂=CH₂) to an active propagating center, forming a long macromolecular polymer chain (-CH₂–CH₂-)ₙ (polyethylene) without eliminating any small byproduct molecules.
Free-radical polymerization proceeds through three kinetic stages: 1) Initiation, homolytic cleavage of an initiator I₂ → 2R^bullet and attack on the first monomer R^bullet + CH₂=CH₂ → R–CH₂–CH₂^bullet; 2) Propagation, rapid sequential monomer addition to the active radical tip at rate vₚ = kₚ [M][R^bullet] ∝ [M]√([I₂]); 3) Termination via radical combination or disproportionation.
In each propagation step, a weaker monomer π-bond (268 kJ/mol, planar sp² carbon, 1.34 Å) converts into a stronger backbone C–C σ-bond (348 kJ/mol, tetrahedral sp³ carbon, 109.5^°, 1.54 Å), making polymerization strongly exothermic (Δ Hₚoly ≈ -93 kJ/mol). The degree of polymerization n governs the molar mass Mₙ = n M₀ and the statistical coil radius of gyration R_g ∝ l₀√(n).
Everyday Analogy
Ethylene monomers CH₂=CH₂ hold onto themselves with two hands (a double bond σ + π). Triggered by a radical initiator, each monomer opens its weaker π-bond to clasp hands with its neighbor, zipping thousands of units into a long polyethylene chain!
Interactive Question & Derivation
What happens to the chemical bonds and carbon hybridization state during the radical polymerization of ethylene n CH₂=CH₂ → (-CH₂–CH₂-)ₙ?
- A: The weaker π-bond of each CH₂=CH₂ monomer cleaves to form new single C–C σ-bonds in the polymer backbone, shifting carbon hybridization from planar sp² (120^°) to tetrahedral sp³ (109.5^°)
- B: Triple C≡C bonds form while eliminating water molecules (polycondensation)
- C: Ethylene polymerization is strongly endothermic because σ-bonds are weaker than π-bonds
Study Hint: During ethylene polymerization, the weaker π-bond cleaves to form new single C–C σ-bonds in the polymer chain, shifting carbon hybridization from planar sp² (120^°) to tetrahedral sp³ (109.5^°).
Proof & Explanation: During radical chain polymerization, each weaker monomer π-bond (E_π ≈ 268 kJ/mol) converts into a stronger backbone C–C single σ-bond (E_σ ≈ 348 kJ/mol). Carbon atoms transition from planar sp² (120^°, 1.34 Å) to tetrahedral sp³ (109.5^°, 1.54 Å), releasing Δ H ≈ -93 kJ/mol of heat per monomer unit.
Key Equations & 3D Simulation Parameters
Mₙ = n M₀, vₚ = kₚ[M][R^bullet] ∝ [M]√([I₂]), R_g ∝ l₀√(n)
- Degree of polymerization n (–CH₂–CH₂– repeat units): 4 … 18 units (default: 10 units)
- Radical initiator concentration [I₂]: 0.5 … 5 mmol/L (default: 2 mmol/L)
- Ethylene monomer concentration [CH₂=CH₂]: 0.5 … 3 mol/L (default: 1.5 mol/L)
- Polymerization reactor temperature T: 300 … 420 K (default: 350 K)